Two-dimensional discrete Markovian fields

Authors:
J. Woods
Affiliations:
-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

A definition of discrete Markovian random fields is formulated analogously to a definition for the continuous case given by Lévy. This definition in the homogeneous Gaussian case leads to a difference equation that sets forth the state of the field in terms of its values on a band of minimum widthP, wherePis the order of the process. The state of the field at position(i,j)is given by the set of values of the nearest neighbors within distancePof the point(i,j). Conversely, given a difference equation satisfying certain conditions relating to stability, there corresponds a homogeneous discrete Markov random field. This theory is applied to the problem of obtaining spectral estimates of a two-dimensional field, given observation over a limited aperture.